Quadrupole oscillation of a single-vortex Bose-Einstein condensate: evidence for Kelvin modes

We study the two transverse quadrupole modes of a cigar-shaped Bose-Einstein condensate with a single centered vortex. We show that the counterrotating mode is more strongly damped than in the absence of a vortex, whereas the corotating mode is not affected appreciably by the vortex. We interpret this result as a decay of the counterrotating quadrupole mode into two excitations of the vortex line, the so-called Kelvin modes. This is supported by direct observation of the vortex line.     

Transverse instability of straight vortex lines in dipolar Bose-Einstein condensates

The physics of vortex lines in dipolar condensates is studied. Because of the nonlocality of the dipolar interaction, the 3D character of the vortex plays a more important role in dipolar gases than in typical short-range interacting ones. In particular, the dipolar interaction significantly affects the stability of the transverse modes of the vortex line. Remarkably, in the presence of a periodic potential along the vortexline, the spectrum of transverse modes shows a rotonlike minimum, which eventually destabilizes the straight vortex when the BEC as a whole is still stable, opening the possibility for new scenarios for vortex-line configurations in dipolar gases.     

Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model

The flexural vibration of the fluid-conveying single-walled carbon nanotube (SWCNT) is derived by the Timoshenko beam model, including rotary inertia and transverse shear deformation. The effects of the flow velocity and the aspect ratio of length to diameter on the vibration frequency and mode shape of the SWCNT are analyzed. Results show that the effects of rotary inertia and transverse shear deformation result in a reduction of the vibration frequencies, especially for higher modes of vibration and short nanotubes. The frequency is also compared with the previous study based on Euler beam model. In addition, if the ratio of length to diameter increased to 60, the influence of the shear deformation and rotary inertia on the mode shape and the resonant frequencies can be neglected. However, the influence is very obvious when the ratio decreased to 20. As the flow velocity of the fluid increases in the vicinity of 2π, the SWCNT reveals the divergence instability. It regains stability when the flow velocity reaches about 9. As the velocity increases further, the SWCNT undergoes a coupled-mode flutter and results in a larger amplitude.     

Astigmatic telescopic transformation of a high-order optical vortex

Properties of an optical vortex light beam formed after the astigmatic telescopic transformation of a circular Laguerre-Gaussian mode are considered both theoretically and experimentally. The beam evolution is found to be in conformity with the general notions on the high-order optical vortex symmetry breakdown. Upon propagation, the asymmetric beam shows a sort of rotation of its transverse profile in accord with the energy circulation in the original circular mode; this process is described on the base of the beam intensity moments and the vortex and asymmetry components of its orbital angular momentum. An l-charged optical vortex converts into |l| secondary first-order vortices positioned on a straight line crossing the beam axis. Orientation of this straight line in the beam cross section and spatial separation of the secondary vortex cores depend on the propagation distance. Morphology (orientation and anisotropy) of all the secondary vortices is the same and depends on the propagation distance; the anisotropy can be characterized by the vortex component of the beam angular momentum. At certain distance, relative separation of secondary vortices with respect to the beam transverse size reaches its maximum that corresponds to the minimum anisotropy of the vortices. The results can be useful in the context of current research of the optical vortex arrays.     

Oscillation spectrum for a single Abrikosov vortex in Josephson media

A spectrum of transverse oscillations of a single vortex filament in a granular type-II superconductor has been investigated theoretically. The oscillation frequency is shown to be highly dependent on characteristics of the Josephson medium and on vortex filament location in a granule. When the Abrikosov vortex enters (leaves) the granule, the spectrum looks like a surface potential barrier. A variation of granulated-medium parameters results in changes of gap size in the excitation spectrum.     

Collective oscillations of vortex lattices in rotating Bose-Einstein condensates

The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates by solving the Bogoliubov-de Gennes equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both approaches allows one to unambiguously identify every observed mode.     

Spin-dependent transverse force on a vortex light beam in an inhomogeneous medium

Spin-dependent effects on vortex light beams propagating in an inhomogeneous medium are demonstrated by solving the full three-component field Maxwell equations using the perturbation analysis. It is found that the hybrid Laguerre–Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams in a cylindrical graded-index medium is investigated. It is shown that the vortex light beam undergoes an additional transverse force acting differently on circular polarized beams with opposite handedness. The wave shape variation with distance taking into account the spin–orbit and nonparaxial effects is analyzed. Effect of long-term periodical revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is demonstrated.     

Spontaneous transverse pattern formation in a microchip laser excited by a doughnut pump profile

A transition from a pure Laguerre–Gaussian (LG) mode to a pattern of optical vortex lattices in a large-Fresnel-number microchip laser is experimentally demonstrated by controlling the cavity Q-factor. The cooperative frequency locking of nearly degenerate modes is found to be a primary process for the generation of the optical vortex lattices in a class-B laser. When the cavity Q-factor is high enough, a LG-like mode and a structure of optical vortex lattices are found to coexist. Competition between coexisting transverse patterns of different symmetry gives rise to chaotic fluctuations. Received: 20 March 2002 / Revised version: 20 May 2002 / Published online: 25 October 2002 RID="*" ID="*"Corresponding author. Fax: +886-35/729134, E-mail: yfchen@cc.nctu.edu.tw     

Multi-dimensional vortex quasi-simple waves

Multi-dimensional vortex modes of a quasi-simple wave solution is presented. These are constructed on the basis of vortex modes for ideal simple waves. A version of 2D Burgers equation is derived which is the same as that obtained for sound quasi-simple waves if neglecting the last term of the latter. Some solutions are explained in physical detail which have a localized traveling behavior. A numerical simulation is shown to support the obtained analytical solutions.     

The effect of a large SWNT diameter distribution on cesium intercalation

Vapor-phase intercalation of a single-walled carbon nanotube sample with Cs was carried out and monitored in situ by Raman spectroscopy. Results indicate that the endpoint of the intercalation was limited by small interstitial gaps in the nanotube bundles. These small-diameter gaps are present because of the significant number of small-diameter nanotubes (0.9-1.0 nm, as calculated from Raman radial breathing mode frequencies) present in the sample. It is not possible to determine from our Raman spectra whether the early endpoint is the result of diffusion limitation or the equilibrium energetics at the endpoint, although some diffusion limitation is observed near the beginning of the reaction. A simple geometric model for expansion of the nanotube bundles under intercalation is presented; this model reproduces, reasonably well, measured expansions reported by others and explains both diffusion- and equilibrium-limited mechanisms in terms of the larger lattice expansion required for smaller-diameter nanotubes. Staging of the intercalation process, in analogy with the staged intercalation of graphite intercalation compounds, is not observed. Instead, the transverse mode peaks undergo a gradual decrease in intensity and a gradual charge transfer- and electronic coupling-induced downshift.     

Plasmon hybridization in metallic nanotubes

We study theoretical formalism of the plasmon hybridization in a metallic nanotube and find an explicit form of the dispersion relation for surface plasmons, in terms of interaction between the bare plasmon modes of the individual surfaces of the nanotubes. In the special case when the longitudinal wave vector is zero (q=0), the plasmon hybridization of a nanotube has a behavior similar to the spherical nanoshell.     

Effective lagrangian and topological interactions in supersolids

We construct a low-energy effective Lagrangian describing zero temperature supersolids. Galilean invariance imposes strict constraints on the form of the effective Lagrangian. We identify a topological term in the Lagrangian that couples superfluid and crystalline modes. For small superfluid fractions, this interaction term is dominant in problems involving defects. As an illustration, we compute the differential cross section of scatterings of low-energy transverse elastic phonons by a superfluid vortex. The result is model independent.     

Phase diagrams of a cylindrical transverse Ising ferrimagnetic nanotube; Effects of surface dilution

Phase diagrams (transition temperature and compensation temperature) of a cylindrical ferrimagnetic nanotube with a negative core–shell interaction, described by the transverse Ising model (TIM), are investigated by the use of the effective-field theory with correlations. The phase diagrams of the system are strongly affected by the surface dilution. The possibility of two compensation points is found in the phase diagram, in contrast to the case of a cylindrical TIM nanowire.     

Entangled double-helix phase

We present a novel phase with an entangled double-helix structure. Beams with this phase have the same transverse patterns as those of interference between two doughnut beams. This proposed method allows a complete set of the superpositions of the doughnut modes or the orbital angular momentum states with different topological orders to be obtained. Furthermore, it introduces a simple continuous and controlled rotation of the transverse patterns by use of a spatial light modulator. It can be used to form a three-dimensional structure by three-dimensional trapping in an optical tweezers setup or to study the quantum characteristics of an optical vortex.     

Well-confined Yb:GdVO4 laser waveguide formed by MeV C ion implantation

The planar waveguide in x-cut Yb:GdVO₄ crystal has been fabricated by 6.0 MeV carbon ion implantation with the fluence of 1 × 10¹⁴ ions/cm² at room temperature. The modes of the waveguide were measured by the prism-coupling method with the wavelength of 633 nm and 1539 nm, respectively. An enhanced ordinary refractive index region was formed with a width of about 4.0 μm beneath the sample surface to act as a waveguide structure. By performing a modal analysis on the observed transverse magnetic polarized modes, it was found that all the transverse magnetic polarized modes can be well-confined inside the waveguide. Strong Yb-related photoluminescence in Yb:GdVO₄ waveguide has been observed at room temperature, which reveals that it exhibits possible applications for integrated active photonic devices.     

Interplay of magneto-elastic and polaronic effects in electronic transport through suspended carbon-nanotube quantum dots

We investigate the electronic transport through a suspended carbon-nanotube quantum dot. In the presence of a magnetic field perpendicular to the nanotube and a nearby metallic gate, two forces act on the electrons: the Laplace and the electrostatic force. They both induce coupling between the electrons and the mechanical transverse oscillation modes. We find that the difference between the two mechanisms appears in the cotunneling current.     

Scattering cross section of metallic two-walled carbon nanotubes

The electromagnetic wave scattering from a metallic two-walled carbon nanotube is studied. The system is assumed to be illuminated by either a transverse magnetic or a transverse electric wave. Boundary-value method is used to evaluate the scattering characteristics of the system. Electronic excitations of each wall of nanotube are modeled as an infinitesimally thin cylindrical layer of the free-electron gas described previously by means of the linearized fluid theory. The computed results include the evaluation of the normalized scattering width of both transverse magnetic and transverse electric uniform plane wave by system at normal incidences.     

Effect of vacancy defect on electrical properties of chiral single-walled carbon nanotube under external electrical field

Ab initio calculations demonstrated that the energy gap modulation of a chiral carbon nanotube with mono-vacancy defect can be achieved by applying a transverse electric field. The bandstructure of this defective carbon nanotube varying due to the external electric field is distinctly different from those of the perfect nanotube and defective zigzag nanotube. This variation in bandstructure strongly depends on not only the chirality of the nanotube and also the applied direction of the transverse electric field. A mechanism is proposed to explain the response of the local energy gap between the valence band maximum state and the local gap state under external electric field. Several potential applications of these phenomena are discussed.     

Non-one-dimensional optical solitons and ideal fluid dynamics

Influence of transverse effects on the propagation of light beams in gradient glass fiber and on the pulsed mode of the second harmonic generation is investigated. Within the approaches under consideration the equations for the pulse or beam field envelopes are reduced to a system of hydrodynamictype equations for amplitudes and eikonals. These equations are used to describe the vortex and non-vortex beam channeling modes and the propagation of light bullets.